(84.)Notwithstanding these and other advantages attending the new engines, Boulton and Watt experienced difficulties all but insurmountable in getting them into use. No manufactory existed in the country possessing machinery capable of[Pg153]executing with the necessary precision the valves and other parts which required exact execution, and the patentees were compelled to construct machinery at Soho for this purpose; and even after they succeeded in getting the cylinders properly bored, the piston rods exactly turned and polished, the spindle valves constructed so as to be steam-tight, and every other arrangement completed which was necessary for the efficiency of the machine, the novelty of the engine, and the difficulty which was supposed to attend its maintenance in good working order, formed strong objections to its adoption.
To remove such objections, great sacrifices were necessary on the part of Boulton and Watt; and they accordingly resolved to undertake the construction of the new engines without any profit, giving them to the parties requiring their use at first cost, on the condition of being remunerated by a small share of what they would save in fuel.
"We have no objection," writes Mr. Boulton, "to contract with the Carron Company to direct the making of an engine to return the water for their mills.* * * *We do not aim at profits in engine building, but shall take our profits out of the saving of fuel; so that if we save nothing, we shall take nothing. Our terms are as follows: we will make all the necessary plans, sections, and elevations for the building, and for the engine with its appurtenances, specifying all cast and forged iron work, and every other particular relative to the engine. We will give all necessary directions to your workmen, which they must implicitly obey. We will execute, for a stipulated price, the valves, and all other parts which may·require exact execution, at Soho; we will see that all the parts are put together, and set to work, properly; we will keep our own work in repair for one year, and we have no other objection to seven years than the inconvenience of the distance. We will guarantee that the engine so constructed shall raise at least 20,000 cubic feet of water twenty-four feet high with each hundred weight of coals burnt.
"When all this is done, a fair and candid comparison shall be made between it, and your own engine, or any other engine in Scotland, from which comparison the amount of savings in fuel shall be estimated, and that amount being[Pg154]divided into three parts, we shall be entitled to one of those parts, in recompense for our patent licence, our drawings, &c. &c. Our own share of savings shall be estimated in money, according to the value of your coals delivered under the boiler, and you shall annually pay us that sum, during twenty-five years from the day you begin to work; provided you continue the use of the engine so long. And in case you sell the engine, or remove it to any other place, you must previously give us notice, for we shall then be entitled to our third of the savings of fuel, according to the value of coals at such new place. This is a necessary condition, otherwise the engine which we make for you at an expense of two thousand pounds may be sold in Cornwall for ten thousand pounds.
"Such parts of the engine as we execute at Soho we will be paid for at a fair price; I conclude, from all the observations I have had an opportunity of making, that our engines are four times better than the common engines. In boilers, which are a very expensive article, the savings will be in proportion to the savings of coal. If you compare our engine with the common engine (not in size, but in power), you will find the original expense of erecting one to be nearly the same.
"Mr. Wilkinson has bored us several cylinders, almost without error; that of fifty inches diameter, which we put up at Tipton, does not err the thickness of an old shilling in any part; so that you must either improve your method of boring, or we must furnish the cylinder to you."
The reluctance of mining companies to relinquish the old engines, even on these terms, led them to propose to Mr. Watt to grant them a licence for the use of his condenser, to be applied to the atmospheric engine, without the introduction of other improvements. Such a proposition was made to him by Mr. Smeaton, in the year 1778, to which he returned the following answer:—
"I have several times considered the propriety of the application of my condensers to common engines, and have made experiments with that view upon our engine at Soho, but have never found such results as would induce me to try[Pg155]it any where else; and, in consequence, we refused to make that application to Wheal Virgin engines in Cornwall, and to some others; our reasons were, that though it might have enabled them to have gone deeper with their present engines, yet, the savings of fuel would not have been great, in comparison to the complete machine. By adding condensers to engines that were not in good order, our engine would have been introduced into that country (which we look upon as our richest mine) in an unfavourable point of view, and without such profits as would have been satisfactory either to us or to the adventurers; and if we had granted the use of condensers to one, we must have done so to all, and thereby have curtailed our profits, and perhaps injured our reputation. Besides, where a new engine is to be erected, and to be equally well executed in point of workmanship and materials, an engine of the same power cannot be constructed materially cheaper on the old plan than on ours; for our boiler and cylinder are much smaller, and the building, the lever, the chains, together with all the pump and pit work, are only the same.* * * *
"We charge our profits in proportion to the saving made in fuel by our engine, when compared with a common one which burns the same kind of coals; we ask one third of these savings to be paid us annually, or half yearly; the payment being redeemable in the option of our employer, at ten years' purchase; and when the coals are low priced, we should also make some charge as engineers. In all these comparisons our own interest has made us except your (Mr. Smeaton) improved engines, unless we were allowed a greater proportion of the savings."
Their exertions to improve the manufacture of engines at Soho is shown by the following letter from Mr. Boulton, in the same correspondence to Mr. Smeaton:—
"We are systematising the business of engine making, as we have done before in the button manufactory; we are training up workmen, and making tools and machines to form the different parts of Mr. Watt's engines with more accuracy, and at a cheaper rate than can possibly be done by the ordinary methods of working. Our workshop and apparatus will be of[Pg156]sufficient extent to execute all the engines which are likely to be soon wanted in this country; and it will not be worth the expense for any other engineers to erect similar works, for that would be like building a mill to grind a bushel of corn.
"I can assure you from experience, that our small engine at Soho is capable of raising 500,000 cubic feet of water 1 foot high with every 112 lbs. of coals, and we are in hopes of doing much more. Mr. Watt's engine has a very great advantage in mines, which are continually working deeper: suppose, for instance, that a mine is 50 fathoms deep, you may have an engine which will be equal to draining the water when the mine is worked, to 100 fathoms deep, and yet you can constantly adapt the engine to its load, whether it be 50 or 100 fathoms, or any intermediate depth; and the consumption of coals will be less in proportion when working at the lesser than at the greater depths; supposing it works, as our engines generally do, at 11 lbs. per square inch, when the mine becomes 100 fathoms deep."
(85.)The great improvement which has been introduced within the last half century, in the details of Watt's steam engine, will be rendered manifest by comparing the effects of a given weight of fuel here supplied by Mr. Boulton with the effects which the same weight of fuel is now known to produce in the best pumping engines worked in Cornwall. One of these engines, in good working order, has been known to raise 125,000,000 lbs. 1 foot high, by the combustion of a bushel of coals. But the average performance of even the best engines is below this amount. If we take it at 90,000,000, this will be equivalent to the weight of about11⁄2million cubic feet of water, a bushel of coals being3⁄4cwt. It will therefore follow that, with the present engines, one hundred weight of coals is capable of raising about two million cubic feet of water one foot high, being a duty four times that assigned to the early engines by Mr. Boulton.
(86.)At the time that Watt, in conjunction with Dr. Roebuck, obtained the patent for his improved engine, the idea occurred to him, that the steam which had impelled the piston in its descent rushed from the cylinder with a mechanical force much more than sufficient to overcome any resistance[Pg157]which it had to encounter in its passage to the condenser; and that such force might be rendered available as a moving power, in addition to that already obtained from the steam during the stroke of the piston. This notion involved the whole principle of the expansive action of steam, which subsequently proved to be of such importance in the performance of steam engines. Watt was, however, so much engrossed at that time, and subsequently, by the difficulties he had to encounter in the construction of his engines, that he did not attempt to bring this principle into operation. It was not until after he had organised that part of the establishment at Soho which was appropriated to the manufacture of steam engines, that he proceeded to apply the expansive principle. Since the date of the patent which he took out for this (1782), was subsequent to the application of the same principle by another engineer, named Hornblower, it is right to state, that the claim of Mr. Watt to this important step in the improvement of the steam engine, is established by a letter addressed by him to Dr. Small, of Birmingham, dated Glasgow, May, 1769:—
"I mentioned to you a method of still doubling the effect of the steam, and that tolerably easy, by using the power of steam rushing into a vacuum, at present lost. This would do little more than double the effect, but it would too much enlarge the vessels to use it all: it is peculiarly applicable to wheel engines, and may supply the want of a condenser, where the force of steam only is used; for open one of the steam valves, and admit steam until one fourth of the distance between it and the next valve is filled with steam, then shut the valve, and the steam will continue to expand, and to press round the wheel, with a diminishing power, ending in one fourth of its first exertion. The sum of the series you will find greater than one half, though only one fourth of steam was used. The power will indeed be unequal, but this can be remedied by a fly, or by several other means."
In 1776 the engine, which had been then recently erected at Soho, was adapted to act upon the principle of expansion. When the piston had been pressed down in the cylinder for a certain portion of the stroke, the further supply of steam[Pg158]from the boiler was cut off, by closing the upper steam valve, and the remainder of the stroke was accomplished by the expansive power of the steam which had already been introduced into the cylinder.
(87.)To make this method of applying the force of steam intelligible, some previous explanation of mechanical principles will be necessary.
If a body which offers a certain resistance be urged by a certain moving force, the motion which it will receive will depend on the relation between the energy of the moving force and the amount of the resistance opposed to it. If the moving force be precisely equal to the resistance, the motion which the body will receive will be perfectly uniform.
If the energy of the moving force be greater than the resistance, then its surplus or excess above the amount of resistance will be expended in imparting momentum to the mass of the body moved, and the latter will, consequently, continually acquire augmented speed. The motion of the body will, therefore, be in this case accelerated.
If the energy of the moving force be less in amount than the resistance, then all that portion of the resistance which exceeds the amount of the moving force will be expended in depriving the mass of the body of momentum, and the body will therefore be moved with continually diminished speed until it be brought to rest.
(88.)Whenever, therefore, a uniform motion is produced in a body, it may be taken as an indication of the equality of the moving force to the resistance; and, on the other hand, according as the speed of the body is augmented or diminished, it may be inferred that the energy of the moving force has been greater or less than the resistance.
It is an error to suppose that rest is the only condition possible for a body to assume when under the operation of two or more mechanical forces which are in equilibrium. By the laws of motion the state of a body which is not under the operation of any external force must be either in a state of rest or of uniform motion. Whichever be its state, it will suffer no change if the body be brought under the operation of two or more forces which are in equilibrium; for to suppose[Pg159]such forces to produce any change in the state of the body, whether from rest to motion, orvice versâ, or in the velocity of the motion which the body may have previously had, would be equivalent to a supposition that the forces applied to the body being in equilibrium were capable of producing a dynamical effect, which would be a contradiction in terms. This, though not always clearly understood by mere practical men, or by persons superficially informed, is, in fact, among the fundamental principles of mechanical science.
(89.)When the piston is at the top of the cylinder, and about to commence its motion downwards, the steam acting upon it will have not only to overcome the resistance arising from the friction of the various parts of the engine, but will also have to put in motion the whole mass of matter of the piston pump rods, pump pistons, and the column of water in the pump barrels. Besides imparting to this mass the momentum corresponding to the velocity with which it will be moved, it will also have to encounter the resistance due to the preponderance of the weight of the water and pump rods over that of the steam piston. The pressure of steam, therefore, upon the piston at the commencement of the stroke must, in accordance with the mechanical principles just explained, have a greater force than is equal to all the resistances which it would have to overcome, supposing the mass to be moving at a uniform velocity. The moving force, therefore, being greater than the resistance, the mass, when put in motion, will necessarily move with a gradually augmented speed, and the piston of the engine which has been described in the last chapter would necessarily move from the top to the bottom of the cylinder with an accelerated motion, having at the moment of its arrival at the bottom a greater velocity than at any other part of the stroke. As the piston and all the matter which it has put in motion must at this point come to rest, the momentum of the moving mass must necessarily expend itself on some part of the machinery, and would be so much mechanical force lost. It is evident, therefore, independently of any consideration of the expansive principle, to which we shall presently refer, that the action of the[Pg160]moving power in the descent of the piston ought to be suspended before the arrival of the piston at the bottom of the cylinder, in order to allow the momentum of the mass which is in motion to expend itself, and to allow the piston to come gradually to rest at the termination of the stroke.
Thus, if we were to suppose that after the piston had descended through three fourths of the whole length of the cylinder, and had acquired a certain velocity, the steam above it were suddenly condensed, so as to leave a vacuum both above and below it, the piston, being then subject to no impelling force, would still move downwards, in virtue of the momentum it had acquired, until the resistance would deprive it of that momentum, and bring it to rest; and if the remaining fourth part of the cylinder were necessary for the accomplishment of this, then it is evident that that part of the stroke would be accomplished without further expenditure of the moving power.
In fact, this part of the stroke would be made by the expenditure of that excess of moving power, which, at the commencement of the stroke, had been employed in putting the machinery and its load in motion, and in subsequently accelerating that motion.
Although under such circumstances the resistance, during the operation of the moving power, shall not have been at any time equal to the moving power, since while the motion was accelerated it was less, and while retarded greater than that power, yet as the whole moving power has been expended upon the resistance, the mechanical effect which the moving power has produced under such circumstances will be equal to the actual amount of that power. If in an engine of this kind the steam was not cut off till the conclusion of the stroke, a part of the moving power would be lost upon those fixed points in the machinery which would sustain the shock produced by the instantaneous cessation of motion at the end of the stroke.
Independently, therefore, of any consideration of the expansive principle, it appears that, in an engine of this kind, the steam ought to be cut off before the completion of the stroke.[Pg161]
Fig. 28.
Fig. 28.
(90.)To render the expansive action of steam intelligible, letA B(fig.28.) represent a cylinder whose area we will suppose, for the sake of illustration, to be a square foot, and whose length,A B, shall also be a foot. If steam of a pressure equal to the atmosphere be supplied to this cylinder, it will exert a pressure of about one ton on the piston; and if such steam be uniformly supplied from the boiler, the piston will be moved fromAtoBwith the force of one ton, and that motion will be uniform if the piston be opposed throughout the same space by a resistance equal to a ton. When the piston has arrived atB, let us suppose that the further supply of steam from the boiler is stopped by closing the upper steam valve, and let us also suppose the cylinder to be continued downwards so thatB Cshall be equal toA B, and suppose thatB Chas been previously in communication with the condenser, and is therefore a vacuum. The piston atBwill then be urged with a force of one ton downwards, and as it descends the steam above it will be diffused through an increased volume, and will consequently acquire a diminished pressure. We shall, for the present, assume that this diminution of pressure follows the law of elastic fluids in general; that it will be decreased in the same proportion as the volume of the steam is augmented. While the piston, therefore, moves fromBdownwards it will be urged by a continually decreasing force. Let us suppose, that by some expedient, it is also subject to a continually decreasing resistance, and that this resistance decreases in the same proportion as the force which urges the piston. In that case the motion of the piston would continue uniform. When the piston would arrive atP′, the middle of the second cylinder, then the space occupied by the steam being increased in the proportion of 2 to 3, the pressure on the piston would be diminished in the proportion of 3 to 2, and the pressure at B being one ton, it would be two-thirds of a ton atP′. In like manner when the piston would arrive atC, the space occupied by the steam being double that which[Pg162]it occupied when the piston was atB, the pressure of the steam would be half its pressure atB, and therefore at the termination of the stroke, the pressure on the piston would be half a ton.
If the space fromBtoC, through which the steam is here supposed to act expansively, be divided into ten equal parts, the pressure on the piston at the moment of passing each of those divisions would be calculated upon the same principle as in the cases now mentioned. After moving through the first division, the volume of the steam would be increased in the proportion of 10 to 11, and therefore its pressure would be diminished in the proportion of 11 to 10. The pressure, therefore, driving the piston at the end of the first of these ten divisions would be10⁄11thsof a ton. In like manner, its pressure at the second of the divisions would be10⁄12thsof a ton, and the third10⁄13thsof a ton; and so on, as indicated in the figure.
Now if the pressure of the steam through each of these divisions were to continue uniform, and, instead of gradually diminishing, to suffer a sudden change in passing from one division to another, then the mechanical effect produced fromBtoCwould be obtained by taking a mean or average of the several pressures throughout each of the ten divisions. In the present case it has been supposed that the force on the piston atBwas 2240 pounds. To obtain the pressure in pounds corresponding to each of the successive divisions, it will therefore only be necessary to multiply 2240 by 10, and to divide it successively by 11, 12, 13, &c. The pressures, therefore, in pounds, at each of the ten divisions, will be as follows:—
If the mean of these be taken by adding them together[Pg163]and dividing by 10, it will be found to be 1498 pounds. It appears, therefore, that the pressures through each of the ten divisions being supposed to be uniform (which however, strictly, they are not,) the mechanical effect of the steam fromBtoCwould be the same as if it acted uniformly throughout that space upon the piston with a force of about 1500 pounds, being rather less than three-fourths of its whole effect fromAtoB.
But it is evident that this principle will be equally applicable if the second cylinder had any other proportion to the first. Thus it might be twice the length of the first; and in that case, a further mechanical effect would be obtained from the expansion of the steam.
The more accurate method of calculating the effect of the expansion fromBtoC, would involve more advanced mathematical principles than could properly be introduced here; but the result of such a computation would be that the actual average effect of the steam fromBtoCwould be equal to a uniform pressure through that space, amounting to one thousand five hundred and forty-five pounds, being greater than the result of the above computation, the difference being due to the expansive action through each of the ten divisions, which was omitted in the above computation.
(91.)It is evident that the expansive principle, as here explained, involves the condition of a variation in the intensity of the moving power. Thus, if the steam act with a uniform energy on the piston so long as its supply from the boiler continues, the moment that supply is stopped, by closing the steam valve, the steam contained in the cylinder will fill a gradually increasing volume by the motion of the piston, and therefore will act above the piston with a gradually decreasing energy. If the resistance to the moving power produced by the load, friction, &c. be not subject to a variation corresponding precisely to such variation in the moving power, then the consequence must be that the motion imparted to the load will cease to be uniform. If the energy of the moving power at any part of the stroke be greater than the resistance, the motion produced will be accelerated; if it be less, the motion will be retarded; and if it be at one time greater, and another[Pg164]time less, as will probably happen, then the motion will be alternately accelerated and retarded. This variation in the speed of the body moved will not, however, affect the mechanical effect produced by the power, provided that the momentum imparted to the moving mass be allowed to expend itself at the end of the stroke, so that the piston may be brought to rest as nearly as possible by the resistance of the load, and not by any shock on any fixed points in the machine. This is an object which, consequently, should be aimed at with a view to the economy of power, independently of other considerations connected with the wear and tear of the machinery. So long as the engine is only applied to the operation of pumping water, great regularity of motion is not essential, and, therefore, the variation of speed which appears to be an almost inevitable consequence of any extensive application of the expansive principle, is of little importance. In the patent which Watt took out for the application of the expansive principle, he specified several methods of producing a uniform effect upon a uniform resistance, notwithstanding the variation of the energy of the power which necessarily attended the expansion of the steam. This he proposed to accomplish by various mechanical means, some of which had been previously applied to the equalisation of a varying power. One consisted in causing the piston to act on a lever, which should have an arm of variable length, the length increasing in the same proportion as the energy of the moving power diminished. This was an expedient which had been already applied in mechanics for the purpose of equalising a varying power. A well-known example of it is presented in the main-spring and fuzee of a watch. According as the watch goes down, the main-spring becomes relaxed, and its force is diminished; but, at the same time, the chain by which it drives the fuzee acts upon a wheel or circle, having a diameter increased in the same proportion as the energy of the spring is diminished.
Another expedient consisted in causing the moving power, when acting with greatest energy, to lift a weight which should be allowed to descend again, assisting the piston when the energy of the moving force was diminished.[Pg165]
Another method consisted in causing the moving force, when acting with greatest energy, to impart momentum to a mass of inert matter, which should be made to restore the same force when the moving power was more enfeebled. We shall not more than allude here to these contrivances proposed by Watt, since their application has never been found advantageous in cases where the expansive principle is used.
(92.)The application of the expansive principle in the engines constructed by Boulton and Watt, was always very limited, by reason of their confining themselves to the use of steam having a pressure not much exceeding that of the atmosphere. If the principle of expansion, as above explained, be attentively considered, it will be evident that the extent of its application will mainly depend on the density and pressure of the steam admitted from the boiler. If the density and pressure be not considerable when the steam is cut off, the extent of its subsequent expansion will be proportionally limited. It was in consequence of this, that this principle from which considerable economy of power has been derived, was applied with much less advantage by Mr. Watt than it has since been by others, who have adopted the use of steam of much higher pressure. In the engines of Boulton and Watt, where the expansive principle was applied, the steam was cut off after the piston had performed from one half to two thirds of the stroke, according to the circumstances under which the engine was worked. The decreasing pressure produced by expansion was, in this case, especially with the larger class of engines, little more than would be necessary to allow the momentum of the mass moved to spend itself, before the arrival of the piston at the end of the stroke.
Subsequently, however, boilers producing steam of much higher pressure were applied, and the steam was cut off when the piston had performed a much smaller part of the whole stroke. The great theatre of these experiments and improvements has been the mining districts in Cornwall, where, instead of working with steam of a pressure not much exceeding that of the atmosphere, it has been found advantageous to use steam whose pressure is at least four times as great as[Pg166]that of the atmosphere; and instead of limiting its expansion to the last half or fourth of the stroke, it is cut off after the piston has performed one fourth part of the stroke or less, all the remainder of the stroke being accomplished by the expansive power of the steam, and by momentum.
BRIDGE OVER THE CLYDE AT HAMILTON,DESIGNED BY WATT.
BRIDGE OVER THE CLYDE AT HAMILTON,DESIGNED BY WATT.
DOUBLE-ACTING ENGINE,ZINC WORKS, CITY ROAD, LONDON.
DOUBLE-ACTING ENGINE,ZINC WORKS, CITY ROAD, LONDON.
[Pg167]TOCINX
PROPERTIES OF STEAM.—COMMON STEAM.—SUPERHEATED STEAM.—LAW OF DALTON AND GAY LUSSAC.—LAW OF MARIOTTE.—RELATION BETWEEN TEMPERATURE AND PRESSURE OF COMMON STEAM.—EFFECTS OF THE EXPANSION OF COMMON STEAM.—MECHANICAL EFFECTS OF STEAM.—METHOD OF EQUALISING THE EXPANSIVE FORCE.—HORNBLOWER'S ENGINE.—WOOLF'S ENGINE.—WATT'S ATTEMPTS TO EXTEND THE STEAM ENGINE TO MANUFACTURES.—PAPIN'S PROJECTED APPLICATIONS OF THE STEAM ENGINE.—SAVERY'S APPLICATIONS OF THE ENGINE TO MOVE MACHINERY.—JONATHAN HULL'S APPLICATION TO WATER WHEELS.—STEWART'S APPLICATION OF THE ENGINE TO MILL WORK.—WASHBOROUGH'S APPLICATION OF THE FLY WHEEL AND CRANK.—WATT'S SECOND PATENT.—DOUBLE-ACTION VALVES.
(93.)Since the application of the expansive action of steam involves the consideration of its properties when it ceases to be in contact with the water from which it was produced, and likewise the variation of its pressure in different states of[Pg168]density and at different temperatures, it is necessary here to explain some of the most important of these properties of vapour.
Steam may exist in two states, distinguished from each other by the following circumstances:—
1st. It may be such that the abstraction from it of any portion of heat, however small, will cause its partial condensation.
2d. It may be such as to admit of the abstraction of heat from it without undergoing any other change than that which air would undergo under like circumstances, viz. a diminution of temperature and pressure.
(94.)We shall call, for distinction, the formerCommon Steam, and the latterSuperheated Steam.
Fig. 29.
Fig. 29.
To explain the circumstances out of which these properties arise, letB(fig.29.) be imagined to be a vessel filled with water, communicating by a pipe and stopcock with another vesselA, which in the commencement of the process may be conceived to be filled with air. LetDbe a pipe and stopcock at the top of this vessel. If the vesselBbe heated, and the two cocks be opened, the steam proceeding from the water inBwill blow the air out of the vesselAthrough the open stopcockD, in the same manner as air is blown from a steam engine. When the vesselAby these means has been filled with pure steam, let both stopcocks be closed. If the steam inA, under these circumstances, have a pressure of 15 lbs. per square inch, its temperature will be found to be 213°. Now, if any heat be abstracted from this steam, its temperature will fall, and a portion of it will be reconverted into water.
Again, suppose the vesselAto be filled with pure steam which has been produced from the heated water inB, the stopcockCbeing open. Let the stopcockCbe then closed, and the water inBbe heated to a higher temperature, the temperature and pressure of the steam inAbeing observed. If the stopcockCbe now opened, the steam inAwill be immediately observed to rise to the more elevated temperature which has been imparted to the water inB, and at the same time it will acquire an increased pressure.[Pg169]
The increase of temperature which it has received would of itself produce an increased pressure; but that this is not the sole cause of the augmented pressure in the present case might be proved by weighing the vesselA. It would be found to have increased weight, which could only arise from its having received from the water inBan additional quantity of vapour. The increased pressure therefore, which the steam inAhas acquired, is due conjointly to its increased density and its increased temperature. In general, if the water in the vesselBbe raised or lowered in temperature, the steam in the vesselAwill rise and fall in temperature in a corresponding manner, always having the same temperature as the water inB. If the weight of the vesselAwere observed, it would be found to increase with every increase of temperature, and to diminish with every diminution of temperature, proving that the augmented temperature of the water inBproduces an augmented density of the steam inA. The same pressure would be found always to correspond to the same temperature and density, so that if the numerical amount of any one of the three quantities, the temperature, the pressure, or the density, were known, the other two must necessarily be determined, the same temperature always corresponding to the same pressure, andvice versâ. And in like manner, steam produced under these circumstances of the same density cannot have different pressures. It must be observed that the steam here produced receives all the heat which it possesses from the water from which it is raised. Now it is easily demonstrable, that this is the least quantity of heat which is compatible with the steam maintaining the vaporous form; for if the stopcockCbe closed so as to separate the steam inAfrom the water inB, and that any portion of heat, however small, be then abstracted from the steam inA, some portion of the steam will be reconverted into water.
This then, according to the definition already given, isCommon Steam.
(95.)Let us now suppose that the vesselA, being in communication with the vesselBby the open stopcock, has been filled with pure steam of any given temperature. The steam which it thus contains will be common steam, and, as has been[Pg170]shown (94.), it cannot lose any portion of heat, however small, without being partially condensed; but let the stopcockCbe closed, and let the steam inAbe then exposed to any source of heat by which its temperature may be raised any required number of degrees. From the steam thus obtained heat may be abstracted without producing any condensation; and such abstraction of heat may be continued without producing condensation, until the steam is cooled down to that temperature at which it was raised from the water inB, when the stopcockCwas opened. Any further reduction of temperature would be attended with condensation.
If after increasing the temperature of the steam inA, the stopcockCbeing shut so as to render it superheated steam, its pressure be observed, the pressure will be found to be increased, but not to that amount which it would have been increased had the steam inAbeen raised to the same temperature by heating the water inBto that temperature, and keeping the stopcock open. In fact, its present augmented pressure will be due only to its increased temperature, since its density remains unchanged. But if in these circumstances the stopcockCbe suddenly opened, the pressure of the steam inAwill as suddenly rise to that pressure which in common steam corresponds to its temperature; and if the vesselAwere weighed, it would be found to have increased in weight, proving that the steam contained in it has received increased density by an increased quantity of vapour proceeding from the water inA. In fact, by opening the stopcock the steam which was before superheated steam, has become common steam. It has the greatest density which steam of that temperature can have; and consequently, if any heat be abstracted from it, a partial condensation will ensue.
To render these general principles more intelligible, let us suppose that the water inBis raised to the temperature of 213°, the stopcockCbeing open; the vesselAwill then be filled with steam of the same temperature, and having a pressure of 15 lbs. per square inch. This will be common steam. If the stopcock be now closed, and the whole apparatus be exposed to the temperature of 243°; the steam inAwill preserve the same density, but its pressure will be[Pg171]increased from 15 lbs. to a little more than 16 lbs. per square inch. Let the stopcockCbe then opened and while the temperature of the steam inAshall continue to be 243°, the pressure will suddenly rise from 16 lbs. to about 26 lbs. per square inch. The weight of the steam inAwill be at the same time increased in the same proportion of 16 to 26 as its pressure. The steam thus produced inAwill then be common steam, and any abstraction of heat from it would be attended with partial condensation.
(96.)The law, according to which the pressure of elastic fluids in general, whether gases or vapours, increases with their temperature, was simultaneously discovered by Dalton and Gay Lussac. If the pressure which the gas or vapour would have at the temperature of melting ice, were expressed by 10,000, then the increase of pressure which it would receive for every degree of temperature by which it would be raised, its volume being supposed to be preserved, would be expressed by2081⁄3. Thus, if the pressure of gas, or vapour, on a surface of a certain magnitude at the temperature of 32° were 10,000 ounces, then the same gas or vapour would acquire an additional pressure of2081⁄3ounces for every degree of temperature which would be imparted to it above 32°. This law is common to all gases and vapours.
It may be objected that water cannot exist in the state of vapour under the usual pressures at so low a temperature as melting ice. This, however, does not hinder the application of the above law, for that law will equally hold good by computing the pressure which the vapour would have if it were a permanent gas, and if it could therefore exist in the elastic form at that low temperature.
(97.)Another law, common to all elastic fluids, and of equal importance with the former, was discovered by Mariotte. By this law it appears that every gas or vapour, so long as its temperature is unchanged, will have a pressure directly proportional to its density. If therefore, while we compress steam into half its volume, we could preserve its temperature unaltered, we should increase its pressure in a two-fold proportion; but if the process of compression should cause its temperature to increase,[Pg172]then its increase of pressure will be greater than its increase of density, since it will be due conjointly to the increase of density and to the increase of temperature. In this case the increased pressure may be deduced from the combined application of the two laws just explained; that of Mariotte will determine that increase of pressure which is due to the increase of density, and that of Dalton and Gay Lussac will determine the further increase of pressure which will be due to the increase of temperature. The full investigation of these effects, and the formulæ expressing them, will be found in the Appendix to this volume.
(98.)The fixed relations which exist between the temperatures of common steam and its pressure and density, have never been discovered from any general physical principles. The pressures and the densities however, which correspond to a great variety of temperatures throughout the thermometric scale, have been ascertained by extensive series of experiments instituted by philosophers of this and other countries. From a comparison of the temperatures and pressures thus found by experiment, empirical formulæ have been constructed, which exhibit, with an approximation sufficiently close for practice, this relation; and these formulæ may accordingly be used for the computation of tables exhibiting the pressures, temperatures, and densities of common steam; and such tables will have sufficient numerical accuracy for all practical purposes. These formulæ, and the tables resulting from them, will be found in the Appendix to this volume.
(99.)It has been explained, that to effect the conversion of water into steam, it is only necessary to impart to it as much heat as, added to the temperature which it has, would, if it continued in the liquid form, raise it to the temperature of 1212°. This condition is necessary, and sufficient to effect the transition of water into vapour. If, for example, as much heat were imparted to the water evaporated, as would maintain it in the liquid state to 1300°, then the steam so produced would be superheated steam, having 80° of heat more than is necessary to maintain it in the vaporous form. From such steam, therefore, 80° of heat may be abstracted without producing any condensation.[Pg173]
(100.)Common steam being raised from water at any pressure and temperature, and being afterwards separated from the water, if the same steam be compressed into a small volume, or allowed to expand into a greater volume, it will still maintain its quality of common steam, and will have the same pressure and temperature, whatever volume it may assume, as it would have if immediately raised from water at that pressure. Thus if steam be raised from water under a pressure of 30 lbs. per square inch, and, being separated from the water, be allowed to dilate, until its pressure is reduced to 15 lbs. per square inch, its temperature will then be reduced to 213°, which is that temperature which it would have if immediately raised from water under a pressure of 15 lbs. per square inch; and if any heat be abstracted from such steam, whether under its original pressure, or under the diminished pressure of 15 lbs. per square inch, a condensation will be produced, the amount of which will be the same, if the same quantity of heat be abstracted from the steam. These are consequences which immediately flow from the fact, that the sum of the latent and sensible heats of steam is always the same.[20]
It appears, therefore, that supposing the steam used in an engine to receive no additional heat after it leaves the boiler, however it may be changed in its density by subsequent expansion, it will still retain its character of common steam, and cannot lose any portion of heat, however small, without suffering partial condensation. The mechanical force also exerted by such steam, after expansion, must be computed in the same manner as if it were raised immediately.